A Stigmergic Approach to Solving Dynamic Optimization Problems

Many real-world problems are dynamic. Their solving requires an optimization algorithm. Apart from being able to locate the optimum, as it does in the static sense, it should also detect changes in the environment and track a new optimum. The paper presents a differential ant-based stigmergy algorithm (DASA) developed for solving numerical optimization problems. The DASA was applied to dynamic optimization problems with continuous variables proposed for a special session on evolutionary computation in dynamic and uncertain environments at the 2009 IEEE Congress on Evolutionary Computation held in Trondheim, Norway. Results of using DASA show that it can find reasonable solutions for any problem of the kind. One of its advantages is that there is no need of changing the original algorithm. So, it can be used for both cases of numerical optimization, i.e. static and dynamic. Also, the DASA is not sensible to different types of changes and can be used, when the knowledge about the certain problem is limited, i.e. when only the maximal dimension and input problem parameters are known. The performance of the DASA is compared to that of the following four algorithms: a clustering particle swarm algorithm, self-adaptive differential evolution, evolutionary programming with an ensemble of memories, and dynamic artificial immune algorithm. An advanced statistical procedure for performing all pairwise comparisons between the observed algorithms is used. It can be seen that the DASA does not perform much worse than the self-adaptive differential evolution and much better than the other three algorithms.